Processes and devices of the type explained above are already known in which both the first as well as the second web is wound up onto a roll in each case and unwinds from this roll again. The beginning of the second web is connected with the expiring first web in these known processes and devices by pressing the expiring old web onto the roll of the new web or by pressing the roll of the new web onto the old web. In so doing, the old web then comes into contact with an adhesive strip attached to the circumference of the roll of the new web at the beginning of the new web and then pulls the new web along with it. These known processes and devices, however, have several drawbacks. On the one hand, expensive pivotal bases are necessary in order to be able to move the new roll to the old web. In addition, the speed of the new web roll must be coincided exactly with the speed of the old web before the beginning of the new web is cemented to the old web. For this purpose, it is necessary in most of the devices and processes to reduce the speed of the old web while the new is being connected or to accelerate the new web roll to the necessary speed by means of special driving means. In the case of the known processes and devices, it is not possible either to unwind the new web arbitrarily from its roll such that either the web surface facing the interior of the roll comes to lie on top or the web surface facing the exterior of the roll. Only the web surface facing the exterior of the roll can be connected with the old web. Seen in their entirety, the known processes and devices are unreliable and uneconomical in operation and can only be employed to a limited extent.